Related papers: A Graph Spectral Flow for Computing Nodal Deficien…
Signal processing on graphs is a recent research domain that aims at generalizing classical tools in signal processing, in order to analyze signals evolving on complex domains. Such domains are represented by graphs, for which one can…
Exploring the relationship between geometry and the resonant frequencies of a shape is of interest to pure and applied mathematicians. These resonant frequencies are related to the spectrum of the Laplacian, a partial differential operator.…
Simplicial complexes are generalizations of graphs that describe higher-order network interactions among nodes in the graph. Network dynamics described by graph Laplacian flows have been widely studied in network science and control theory,…
A graph's spectral wavelet signature determines a filtration, and consequently an associated set of extended persistence diagrams. We propose a framework that optimises the choice of wavelet for a dataset of graphs, such that their…
We introduce and study Laplacians on a finite metric graph endowed with generalized densities, that is, measures of finite mass. One important motivation is that this setting provides a common framework for several interesting classes of…
We present a method for proving upper bounds on the eigenvalues of the graph Laplacian. A main step involves choosing an appropriate "Riemannian" metric to uniformize the geometry of the graph. In many interesting cases, the existence of…
Flows in networks (or graphs) play a significant role in numerous computer vision tasks. The scalar-valued edges in these graphs often lead to a loss of information and thereby to limitations in terms of expressiveness. For example,…
In this paper, we study the mean curvature flow of graphs with Neumann boundary condition. The main aim is to use the maximum principle to get the boundary gradient estimate for solutions. In particular, we obtain the corresponding…
In this work we study the geodesic flow on nilmanifolds associated to graphs. We are interested in the construction of first integrals to show complete integrability on some compact quotients. Also examples of integrable geodesic flows and…
We propose a method by which to recover an underlying graph from a set of multivariate wave signals that is discretely sampled from a solution of the graph wave equation. Herein, the graph wave equation is defined with the graph Laplacian,…
The aim of this paper is to propose a novel framework to infer the sheaf Laplacian, including the topology of a graph and the restriction maps, from a set of data observed over the nodes of a graph. The proposed method is based on sheaf…
We give the spectral representation for a class of selfadjoint discrete graph Laplacians $\Delta$, with $\Delta$ depending on a chosen graph $G$ and a conductance function $c$ defined on the edges of $G$. We show that the spectral…
Let $G$ be a simple, connected graph on $n$ vertices, and further assume that $G$ has disjoint cycles. Let $h$ be a real symmetric matrix supported on $G$ (for example, a discrete Schr\"odinger operator). The eigenvalues of $h$ are ordered…
What is the best way to match the nodes of two graphs? This graph alignment problem generalizes graph isomorphism and arises in applications from social network analysis to bioinformatics. Some solutions assume that auxiliary information on…
This paper introduces the notion of local spectral expansion of a simplicial complex as a possible analogue of spectral expansion defined for graphs. We then show that the condition of local spectral expansion for a complex yields various…
In this Thesis, we study the behavior of spectral curves of quantum graphs under certain families of vertex conditions, called the $\delta_s$ family, which we define in this work. We focus on studying two main quantities related to the…
Network-topology inference from (vertex) signal observations is a prominent problem across data-science and engineering disciplines. Most existing schemes assume that observations from all nodes are available, but in many practical…
The Laplacian matrix of a simple graph is the difference of the diagonal matrix of vertex degree and the (0,1) adjacency matrix. In the past decades, the Laplacian spectrum has received much more and more attention, since it has been…
Contrastive learning has emerged as a premier method for learning representations with or without supervision. Recent studies have shown its utility in graph representation learning for pre-training. Despite successes, the understanding of…
The paper is a brief survey of some recent new results and progress of the Laplacian spectra of graphs and complex networks (in particular, random graph and the small world network). The main contents contain the spectral radius of the…